Classically, in order to resolve an equation u≈v over a free monoid X*, we reduce it by a suitable family ℱ of substitutions to a family of equations uf≈vf, f∈ℱ, each involving less variables than u≈v, and then combine solutions of uf≈vf into solutions of u≈v. The problem is to get ℱ in a handy parametrized form. The method we propose consists in parametrizing the path traces in the so called graph of prime equations associated to u≈v. We carry out such a parametrization in the case the prime equations in the graph...

Classically, in order to resolve an equation ≈ over a free
monoid *, we reduce it by a suitable family ℱ of substitutions
to a family of equations ≈ , f∈ℱ, each involving less
variables than ≈ , and then combine solutions of ≈
into solutions of ≈ . The problem is to get ℱ in a handy
form. The method we propose consists in parametrizing the
path traces in the so called associated to
≈ . We carry out such a parametrization in the case the prime
equations in the graph involve at most three...